CBSE Class 10 Mathematics

The Ultimate 50 Topic Masterlist

Standard & Basic

Complete Your Prep: ➜ Class 10 Science ➜ Class 12 Maths

Number Systems & Algebra

Weightage: 20 Marks | Focus: Proofs & Word Problems

Irrationality: Prove that \(\sqrt{2}, \sqrt{3}, \text{ or } \sqrt{5}\) is irrational. Guaranteed
LCM & HCF: Relationship: \( \text{HCF} \times \text{LCM} = \text{Product of numbers} \).
Polynomials: Relationship between zeroes and coefficients (\(\alpha + \beta = -b/a\)).
Linear Equations: Solving for \(x\) and \(y\) using Substitution/Elimination.
Word Problems: Upstream/Downstream and Age-related problems.
Quadratic Equations: Nature of roots using Discriminant (\(D = b^2 – 4ac\)).
Quadratic Formula: Solving equations where factorization is difficult.
Arithmetic Progression (AP): Finding the \(n^{th}\) term (\(a_n\)).
Sum of AP: Sum of first \(n\) terms formula applications. Case Study

Weightage: 15 Marks | Focus: Theorems

Basic Proportionality Theorem (BPT): Statement and Proof. Theorem
Similarity: Criteria for similarity of triangles (AA, SAS, SSS).
Tangent Theorem 1: Tangent is perpendicular to the radius at the point of contact.
Tangent Theorem 2: Lengths of tangents from an external point are equal. Must Do
Circle Problems: Finding angles in a quadrilateral formed by tangents and radii.

Weightage: 6 Marks

Distance Formula: Finding distance between two points or from origin.
Equidistant Points: Finding a point on x-axis or y-axis.
Section Formula: Finding the ratio \(m:n\) or coordinates of division point.
\[ P(x,y) = \left( \frac{m_1x_2 + m_2x_1}{m_1+m_2}, \frac{m_1y_2 + m_2y_1}{m_1+m_2} \right) \]
Mid-point Formula: Application in parallelograms and circles.

Weightage: 12 Marks | Focus: Identities

Ratios: Values of \(\sin, \cos, \tan\) at \(30^\circ, 45^\circ, 60^\circ\).
Identities: Proving questions using \(\sin^2\theta + \cos^2\theta = 1\). 3 Marks
Heights & Distances: Angle of Elevation and Depression problems.
Case Study: Real-life application of trigonometry (Tower/Building). Case Study

Weightage: 10 Marks | Focus: Combination of Solids

Combination of Solids: Surface area of Capsule, Tent, or Toy (Cone + Hemisphere).
Volume: Melting and recasting one solid into another (Sphere to Cylinder).
Formulas: Memorize TSA/CSA of Cylinder, Cone, and Sphere.
\[ \text{Vol of Cone} = \frac{1}{3}\pi r^2h \]
Sector & Segment: Area of sector \(\frac{\theta}{360} \times \pi r^2\) and length of arc.

Weightage: 11 Marks | High Scoring

Mean: Direct Method and Assumed Mean Method.
Mode: Finding Mode of grouped data (Highest frequency).
Median: Missing frequency problems in Median (Total frequency given). 5 Marks
Empirical Formula: \(3 \text{ Median} = \text{Mode} + 2 \text{ Mean}\).
Probability: Problems on Dice, Cards (Face cards), and Coins.

Theorems First: Ensure you can write the proofs of BPT and Tangent Theorem without looking. These are free marks.
Step Marking: In Surface Area questions, write the formula first, then substitute values. Don’t calculate until the final step to simplify \(\pi\) and fractions.
Units: Never forget to write \(cm^2\) for area and \(cm^3\) for volume in the final answer.